Optimal. Leaf size=7 \[ \cos (x)+x \sin (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 4, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {3377, 2718}
\begin {gather*} x \sin (x)+\cos (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2718
Rule 3377
Rubi steps
\begin {align*} \int x \cos (x) \, dx &=x \sin (x)-\int \sin (x) \, dx\\ &=\cos (x)+x \sin (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} \cos (x)+x \sin (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 8, normalized size = 1.14
method | result | size |
default | \(\cos \left (x \right )+x \sin \left (x \right )\) | \(8\) |
risch | \(\cos \left (x \right )+x \sin \left (x \right )\) | \(8\) |
norman | \(\frac {2 x \tan \left (\frac {x}{2}\right )+2}{1+\tan ^{2}\left (\frac {x}{2}\right )}\) | \(21\) |
meijerg | \(2 \sqrt {\pi }\, \left (-\frac {1}{2 \sqrt {\pi }}+\frac {\cos \left (x \right )}{2 \sqrt {\pi }}+\frac {x \sin \left (x \right )}{2 \sqrt {\pi }}\right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 2.06, size = 7, normalized size = 1.00 \begin {gather*} x \sin \left (x\right ) + \cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.48, size = 7, normalized size = 1.00 \begin {gather*} x \sin \left (x\right ) + \cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 7, normalized size = 1.00 \begin {gather*} x \sin {\left (x \right )} + \cos {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.89, size = 7, normalized size = 1.00 \begin {gather*} x \sin \left (x\right ) + \cos \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 7, normalized size = 1.00 \begin {gather*} \cos \left (x\right )+x\,\sin \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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